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 A005355 Number of asymmetric permutation rooted trees with n nodes. (Formerly M2680) 2
 0, 1, 1, 1, 3, 7, 21, 61, 187, 577, 1825, 5831, 18883, 61699, 203429, 675545, 2258291, 7592249, 25656477, 87096661, 296891287, 1015797379, 3487272317, 12008898531, 41471260883, 143588078449, 498343911529, 1733410858955, 6041795275027, 21098924740155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Gilbert Labelle, Counting asymmetric enriched trees, J. Symbolic Comput. 14 (1992), no. 2-3, 211-242. FORMULA Shifts left under transform T where Ta has g.f. (1-A(x^2))/(1-A(x)). MATHEMATICA a[0] = 1; a[1] = 1; a[n_] := a[n] = Sum[a[k]*a[n-k], {k, 1, n-1}] - If[EvenQ[n-1], a[(n-1)/2], 0]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Jan 04 2016 *) CROSSREFS Cf. A004111, A050383. Sequence in context: A183113 A102877 A122983 * A182399 A025235 A129366 Adjacent sequences:  A005352 A005353 A005354 * A005356 A005357 A005358 KEYWORD nonn,nice,easy,eigen AUTHOR EXTENSIONS More terms, formula from Christian G. Bower, Nov 15 1999 STATUS approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)